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Simplifying -1(w2 + -25w + -100) = 0 Reorder the terms: -1(-100 + -25w + w2) = 0 (-100 * -1 + -25w * -1 + w2 * -1) = 0 (100 + 25w + -1w2) = 0 Solving 100 + 25w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -25w + w2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -25w + 100 + w2 = 0 + 100 Reorder the terms: -100 + 100 + -25w + w2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -25w + w2 = 0 + 100 -25w + w2 = 0 + 100 Combine like terms: 0 + 100 = 100 -25w + w2 = 100 The w term is -25w. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25w + 156.25 + w2 = 100 + 156.25 Reorder the terms: 156.25 + -25w + w2 = 100 + 156.25 Combine like terms: 100 + 156.25 = 256.25 156.25 + -25w + w2 = 256.25 Factor a perfect square on the left side: (w + -12.5)(w + -12.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (w + -12.5) equal to 16.007810594 and -16.007810594.Subproblem 1
w + -12.5 = 16.007810594 Simplifying w + -12.5 = 16.007810594 Reorder the terms: -12.5 + w = 16.007810594 Solving -12.5 + w = 16.007810594 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + w = 16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = 16.007810594 + 12.5 w = 16.007810594 + 12.5 Combine like terms: 16.007810594 + 12.5 = 28.507810594 w = 28.507810594 Simplifying w = 28.507810594Subproblem 2
w + -12.5 = -16.007810594 Simplifying w + -12.5 = -16.007810594 Reorder the terms: -12.5 + w = -16.007810594 Solving -12.5 + w = -16.007810594 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + w = -16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = -16.007810594 + 12.5 w = -16.007810594 + 12.5 Combine like terms: -16.007810594 + 12.5 = -3.507810594 w = -3.507810594 Simplifying w = -3.507810594Solution
The solution to the problem is based on the solutions from the subproblems. w = {28.507810594, -3.507810594}
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